Properties

Label 8880p
Number of curves $2$
Conductor $8880$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 8880p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8880.c1 8880p1 \([0, -1, 0, -1861, -58439]\) \(-2785840267264/4273846875\) \(-1094104800000\) \([]\) \(12960\) \(1.0016\) \(\Gamma_0(N)\)-optimal
8880.c2 8880p2 \([0, -1, 0, 15899, 1182985]\) \(1736064508952576/3387451171875\) \(-867187500000000\) \([]\) \(38880\) \(1.5509\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8880p have rank \(1\).

Complex multiplication

The elliptic curves in class 8880p do not have complex multiplication.

Modular form 8880.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} - q^{13} + q^{15} + 6 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.